An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
For a device delivering 15.0 A for 30 seconds, the total charge that flows is 450 coulombs. This corresponds to approximately 2.81 billion billion electrons. Therefore, about 2.81 × 1 0 21 electrons flow through the device during this time.
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The problem involves a circle with a diameter and an inscribed angle.
The inscribed angle theorem is applied, stating that the measure of the inscribed angle is half the measure of its intercepted arc.
Since the intercepted arc is a semicircle ( 18 0 ∘ ), the inscribed angle measures 9 0 ∘ .
Therefore, the missing reason is the inscribed angle theorem. in scr ib e d an g l e t h eore m
Explanation
Problem Analysis We are given a circle O with diameter LN and an inscribed angle LMN. We need to prove that angle LMN is a right angle. The proof is presented in a two-column format, with statements and corresponding reasons. Our task is to identify the missing reason in step 5.
Applying Inscribed Angle Theorem The inscribed angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. In this case, ∠ L MN is an inscribed angle that intercepts arc LN, which is a semicircle. Since the measure of a semicircle is 18 0 ∘ , the measure of ∠ L MN is half of 18 0 ∘ .
Finding the Missing Reason Therefore, m ∠ L MN = 2 1 m L N = 2 1 ( 18 0 ∘ ) = 9 0 ∘ . This means the missing reason in step 5 is the inscribed angle theorem.
Conclusion The missing reason in step 5 is the inscribed angle theorem.
Examples
Imagine you're designing a circular park with a walking path that forms an inscribed angle to a diameter. Knowing that the inscribed angle is always a right angle ( 9 0 ∘ ) helps you plan the path so it meets the diameter at a perfect corner, creating a visually appealing and geometrically sound design. This principle ensures that no matter where the path starts on the circle, as long as it ends on the diameter's endpoints, the angle formed will always be a right angle.
